WASHINGTON — President Barack Obama’s plan to cut payroll taxes for a year would provide big savings for many workers, but it makes Social Security advocates nervous that it could jeopardize the retirement program’s finances.

The plan is part of a package of tax cuts and extended unemployment benefits that Obama negotiated with Senate Republican leaders. It would cut workers’ share of Social Security taxes by nearly one-third for 2011. Workers making $50,000 would get a $1,000 tax cut; those making $100,000 would get a $2,000 tax cut.

The government would borrow about $112 billion to make Social Security whole. Social Security advocates and some lawmakers worry that relying on borrowed money to fund Social Security could eventually force it to compete with other federal programs for scarce dollars, leading to cuts.

Social Security taxes “ought to be held sacrosanct,” said Rep. Earl Pomeroy, D-N.D., chairman of the House Ways and Means subcommittee on Social Security.

“When you start to signal that the (Social Security) tax levels are negotiable, you end up in long-term trouble, I think, in terms of making absolutely certain that the entitlement funding streams are secure,” Pomeroy said.

Social Security is funded by a 6.2 percent payroll tax on the first $106,800 earned by a worker. The tax is matched by employers. The package negotiated by Obama would reduce the tax paid by workers to 4.2 percent for 2011. Employer rates would stay unchanged.

Obama administration officials say a payroll-tax cut is an efficient way to stimulate the economy by immediately increasing take-home pay for about 155 million workers. The nonpartisan Congressional Budget Office agrees, and many business groups and Republicans support it.

“What came out of the compromise was the idea of the payroll-tax holiday, which, frankly, a huge number of economists and other experts had been talking about over the last two years with a lot of support in both political parties,” said Larry Summers, Obama’s chief economic adviser.

The United Auto Workers endorsed the deal, saying, “Working families will likely spend this money in their local communities, creating jobs and stimulating overall growth.”

All workers affected

The payroll-tax cut is part of a larger package negotiated by Obama and GOP lawmakers to extend a sweeping array of George W. Bush-era tax cuts that expire at the end of the month. Some Democratic lawmakers have balked at the plan, saying it is tilted too much in favor of the rich.

The payroll-tax cut would provide relief to any worker earning a wage. It would replace Obama’s Making Work Pay tax credit, which has provided modest increases in most workers’ paychecks for the past two years.

The payroll-tax credit would be more generous to individuals making more than $20,000 and married couples making more than $40,000. For those making less, the payroll-tax cut would be less than the Making Work Pay credit.

Making Work Pay, which expires at the end of the year, gives workers a tax credit of 6.2 percent of their wages, but it is capped at $400 for individuals and $800 for couples. The credit is phased out for individuals making more than $75,000 and couples making more than $150,000.

A worker would have to make $20,000 in wages for the payroll-tax cut to equal the $400 Making Work Pay tax credit; couples would have to make $40,000.

At the wealthy end of the pay scale, workers making $106,800 — the maximum amount of wages subject to Social Security taxes — would see their payroll taxes reduced by $2,136. That worker’s spouse could also get a payroll-tax cut of up to $2,136, if he or she makes at least $106,800.

Debating long-term health

The proposal requires the Treasury Department to replenish Social Security with other government funds, which would have to be borrowed.

“The payroll-tax cut has absolutely no effect on the solvency of Social Security,” said White House economic adviser Jason Furman.

Social Security has accumulated a $2.5 trillion trust fund since the 1980s. But the government has borrowed that money to pay for other programs. The Treasury Department has issued special bonds to Social Security, guaranteeing the money will be repaid, with interest.

As aging baby boomers start to retire and strain the system, advocates worry about future benefit cuts. This year, for the first time since the 1980s, Social Security will pay out more in benefits than it collects in payroll taxes. Without changes, Social Security’s trust funds will run out of money by 2037, according to the trustees who oversee the program.

To save money, the leaders of a bipartisan deficit commission recently proposed a gradual increase in the full retirement age, from 67 to 69, drawing opposition from groups representing older people.

“This 2 percent payroll-tax cut is the beginning of the end of Social Security as we know it,” said the National Committee to Preserve Social Security and Medicare, which is led by former Rep. Barbara Kennelly, D-Conn. “Worker contributions have successfully funded the program for 75 years, and that critical linkage between contributions and benefits is what keeps Social Security a self-funded program.”

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